113. In my Double there is a lot of difference in group size

At 10 feet, Federal Premium OO buckshot has a spread of over 2 feet, yet, Winchester #4 Buckshot spread is less than 4 inches. Diferrent gun, different Load, different Size of pattern.

As far as the Rem 870 goes:
The only thing you can do is go out to the Range and test your Shotgun for yourself. Chokes tend to reduce pattern size. The Modified Cylinder is the least restrictive and will tend to create a larger shot pattern than the Full Choke the 870 came with from the Factory.